Modelling response time in a mental rotation task by gender, physical activity, and task features

Mental rotation (MR) is a spatial skill considered to be a key-component of intellectual ability. Studies have suggested that the response time (RT) in a MR task (MRt) might be influenced, with possible gender differences, by the practice of a physical activity (PA) and depending on the plane, direction, degrees of the MR and the frame of reference to perform it. The present study aimed at examining the respective influences of all these variables on the RT by developing a linear mixed-effect model from the RTs varying according to the MR plane, direction, degrees and frame of reference. The MRt was performed by 96 males and females, all undergraduate students, distributed in three groups (sedentary subjects, artistic gymnasts, and futsal players). The results showed that only gender had a main effect (faster log RT in males), probably task-dependent. The other variables interacted among them showing that: (a) the log RT may be influenced by rotations experienced during PA, in particular during the locomotion on a horizontal ground and (b) such influence mainly depends on the compatibility of the physical rotations experienced with the plane and the degrees of the MRt.


SI.2. Normal quantile plot of the residuals after the log-transformation of the RTs
In the present study, the distribution of the RTs was highly skewed to the right. A log-transformation of the RTs was done in order to develop the statistical model. After the log-transformation, the model residuals were found to be normally distributed (see: Supplementary Figure S7). Figure S1. Normal quantile plot of the residual after the log-transformation (natural logarithm) of the RTs.

SI.3. Comparisons of log RTs
The selected model of the log response-times (log RTs) obtained by the subjects included four interaction (*) effects that were statistically significant: (1) PA*d° (interaction between the physical activity practiced by the subjects and the degrees of the rotation to be imagined); (2) PlaneDir*PA (interaction between the plane and direction of the rotation to be imagined and PA); (3) PlaneDir*d°; (4) PlaneDir*FR (interaction between PlaneDir and the frame of reference used to imagine the rotation).
The examination of each interaction led to a series of comparisons of the log RTs that are detailed below. The multiple comparisons were carried out using the method of Bretz, Hothorn, and Westfall 1 (family-wise error rate set at 5%). Regarding the Estimates (differences in log RT) the values of two standard errors may differ after the third decimal only. The corresponding z-scores and adjusted p-values [single-step method; p (>| |)] are also given.
It should be noted that the difference between two log RTs (Estimate) gives the percentage of variation (PV) from one RT to the other with PV = 100 ´ [exp(Estimate) -1].

SI.4 -Calculation of the DMs
The DMs concerned the differences among the mean log RTs obtained in the horizontal, frontal, and sagittal planes. The mean log RTs were calculated considering: -In the horizontal plane: the log RTs obtained when the mental rotation was performed in the left direction and when it was performed in the right direction; -In the frontal plane: the log RTs obtained when the mental rotation was performed in the left direction and when it was performed in the right direction; -In the sagittal plane: the log RTs obtained when the mental rotation performed was backward directed and when it was forward directed.
Using the estimation of the parameters, the means were calculated just as in an effect plot 2 . The differences were obtained as a linear function of these means and simultaneous inference was carried out using the compmult package based on Bretz, Hothorn, and Westfall 1 .
PlaneDir [plane and direction of the rotation to be imagined, rotation in the frontal plane in the right direction (Fr) or in the left direction (Fl), rotation in the horizontal plane in the right direction (Hr) or in the left direction (Hl), or rotation in the sagittal plane backward (Sb) or forward (Sf) directed, and 3. FR [frame of reference used to imagine the rotation, allocentric FR (Allo) or egocentric FR (Ego)]; -The variables involved in each interaction effect found in the study: 1. PA*d°, 2. PlaneDir*PA, 3.

SI.6. Analysis of the probabilities of success
The analysis focused on the probability of success to approach the error rates. A generalized linear mixed effects model 3 was employed to define the main determinants of the rate of success. The outcome binary variable (success vs failure) was fitted using the binomial family and the logit link function. All explanatory variables were fixed effects and subject was the only random effects. The variables were: -Between-subjects variables: 1. Gender [female (Fe) and male (Ma) subjects], and 2. PA [physical activity regularly practiced by the subjects who were sedentary subjects (Sed), artistic gymnasts (Art), or futsal players (Fut)]; -Within-subjects variables: 1. d° (degrees of the rotation to be imagined, either 90°, or 180°), 2. PlaneDir [plane and direction of the rotation to be imagined, rotation in the frontal plane in the right direction (Fr) or in the left direction (Fl), rotation in the horizontal plane in the right direction (Hr) or in the left direction (Hl), or rotation in the sagittal plane backward (Sb) or forward (Sf) directed, and 3. FR [frame of reference used to imagine the rotation, allocentric FR (Allo) or egocentric FR (Ego)].
Additive effects and order-one interactions were considered for fixed effects.
The statistically significant main effects and interaction effects, when ranked in decreasing order of importance using the Chi sq /df criterion of McCullagh and Nelder 4 were the following: PA*d° (Chi sq /df = 19.7; p < .001), PlaneDir (Chi sq /df = 18.8; p < .001), FR*d° (Chi sq /df = 11.8; p < .001), Gender (Chi sq /df = 11.2; p < .001). The effect-plots for PA*d°, PlaneDir, FR*d°, and Gender are shown by the Figure S3  In addition, the obtained comparisons are given as log odds ratios (differences between logit values).     Table S24. Probabilities of success (Proba.s) for each PlaneDir condition. The PlaneDir conditions led to rotation: in the frontal plane on the left (Fl) or on the right (Fr), in the horizontal plane on the left (Hl) or on the right (Hr), in the sagittal plane on a backward direction (Sb) or forward (Sf). Results are averaged over the levels of: PA, d°, FR, and Gender.  Table S25. Comparisons (Estimates) of the Estimated marginal means among the PlaneDir conditions. These conditions led to rotation: in the frontal plane on the left (Fl) or on the right (Fr), in the horizontal plane on the left (Hl) or on the right (Hr), in the sagittal plane on a backward (Sb) or forward direction (Sf). Results are given on the log odds ratio (not the response) scale. The Estimates (± standard error, SE), the z-ratios, and the p-values are given. Tukey method for comparing a family of six Estimates was used for p-values adjustments.

SI.7 -Supplementary Methods: Familiarization with the experimental MR task
Before each of the three experimental series that have been performed in the present study, the subjects were individually familiarized with the series ( Figure S2) after they were informed that this familiarization was prefiguring the performance of a MRt series. Figure S3. Familiarization with the experimental MR task (MRt). Three sequences, each including a familiarization phase (a. and b.) directly followed by a MRt series (c.), have been performed. From one sequence to another, both the familiarization and the consecutive MRt series varied according to the plane of the rotation that was (relative to the subject and, thereafter, to the avatar): horizontal, as exemplified by the photos above, or frontal, or sagittal. During familiarization, each subject individually used a physical device consisting in an aluminium hoop (1.8 m in diameter) that was materializing the plane of the MR to be performed during the experiment. Each subject memorized the four objects fixed by Velcro® scratches (a yellow disk, a red triangle, a blue square and a green star) and the respective locations of each object relative to him/her [(a.) with a subject standing in the centre of the hoop]. The subject was also trained to imagine which object would be at a predetermined location after a rotation (at 90° or at 180°), in one of the two possible directions in the rotation plane (e.g.: leftward or rightward in the horizontal plane) of either the hoop or the subject (a.). After removal of the objects from the hoop, the memorization of the objects and of their respective locations was verified and each subject was trained again to perform MR, as in the previous phase (b.). Thereafter, each subject realized a series of chronometric MRts, directly derived from this familiarization and which were shown on the screen of a laptop [(c.) showing another subject than a. and b. standing in front of the laptop].
During each phase of familiarization, each subject was initially placed in the middle of a physical device that consisted in a large aluminium hoop ( Figure S3.a.). Depending on the phase of familiarization, the subject stoodup: (a) in front of the plane containing the hoop that was maintained vertically in a support, as close as possible to the hoop (in the F condition), (b) at the centre of the hoop that was placed horizontally to the ground (in the H condition), or (c) one foot on each side of the hoop that was maintained vertically (in the S condition). Four objects were initially placed on the hoop ( Figure S3.a.) at the extremities of two orthogonal diameters of the hoop and the same object was systematically placed, in the F, H and S conditions, respectively: (a) at the feet of the subject, (b) in front of the toes of the subject, and (c) between the feet of the subject. Therefore, relative to the subject, the position of each object on the hoop was easy to define and unambiguous. For example, in the H condition, the four objects were respectively placed ~90cm from: (a) the subject's toes, (b) the subject's heels, (c) the subject's right ankle and (d) the subject's left ankle.
The subjects were asked to determine the object that would be at a predefined place relative to the avatar, after a given MR. Different predefined locations were used, e.g.: above the head or at the feet of the subject in F condition 6 . In each plane condition, each subject was trained to imagine eight different rotations, randomly experimented [i.e.: (two d° conditions) ´ (two Dir conditions) ´ (two FR conditions)]. The objects were initially placed on the hoop ( Figure S3.a.) and then they were removed and imagined by the subject (Figure S3.b.) After familiarization with the MRt in one of the three Plane conditions (H, F, or S), the subject realized the experimental series directly derived from this experience ( Figure S3.c.).
Such sequence was reiterated three times, i.e.: in each Plane condition. The order of the sequences was randomly assigned. Two consecutive sequences of familiarization and MRt series were separated by a five mn rest.
b. c. a.